Q: A projectile is launched at an angle $$\theta$$ above the horizontal with initial speed $$v_0. $$Which equation gives the maximum height $$H$$ reached by the projectile?

$$H = \dfrac{v_0$^2 \sin^2$ \theta}{2g}$$

Q: A $$0.2\ \mathrm{kg}$$ ball is swung in a horizontal circle of radius $$0.5\ \mathrm{m} at a $$speed of $$3\ \mathrm{m/s}. $$What is the centripetal force acting on the ball?

$$F_c = \dfrac{mv^2$}{r} = \dfrac{0.2 \times 9}{0.5} = 3.6\ \mathrm{N}$$

Q: A $$10\ \mathrm{kg}$$ box is pulled across a horizontal surface with a force of $$50\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. If the coefficient of kinetic friction is $$\mu_k = 0.2$$, what is the acceleration of the box?

$$a = \dfrac{F \cos \theta - \mu_k mg}{m} = \dfrac{50 \times 0.866 - 0.2 \times 10 \times 9.8}{10} \approx 0.13\ \mathrm{m/s^2$}$$

Q: A $$0.5\ \mathrm{kg}$$ mass attached to a string is whirled in a vertical circle of radius $$1\ \mathrm{m}. $$What is the minimum speed at the top of the circle to keep the string taut?

$$v_{min} = \sqrt{g r} = \sqrt{9.8 \times 1} \approx 3.13\ \mathrm{m/s}$$

Q: A $$0.1\ \mathrm{kg}$$ ball is dropped from a height of $$2\ \mathrm{m}. $$What is its velocity just before hitting the ground?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 2} \approx 6.26\ \mathrm{m/s}$$

Question 1

A ball is thrown vertically upward with an initial velocity of $$v_0 = 20$$\ \mathrm{m/s}$$. Neglecting air resistance, how long does it take for the ball to reach its maximum height?

Accepted Answer

$$t = \dfrac{v_0$}{g} = \dfrac{20}{9.8} \approx 2.04\ \mathrm{s}$$

Question 2

A car accelerates uniformly from rest to a speed of $$30\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the car's acceleration?

Accepted Answer

$$a = \dfrac{v_f - v_i}{t} = \dfrac{30 - 0}{10} = 3\ \mathrm{m/s^2$}$$

Question 3

A projectile is launched at an angle $$	heta$$ above the horizontal with initial speed $$v_0. $$Which equation gives the maximum height $$H$$ reached by the projectile?

Accepted Answer

$$H = \dfrac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 4

A block of mass $$m$$ slides down a frictionless incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 5

A $$2\ \mathrm{kg}$$ object is attached to a spring with spring constant $$k = 50\ \mathrm{N/m}$$ and oscillates in simple harmonic motion. What is the period of oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{m}{k}} = 2\pi \sqrt{\dfrac{2}{50}} \approx 1.26\ \mathrm{s}$$

Question 6

A $$5\ \mathrm{kg}$$ object moving at $$4\ \mathrm{m/s}$$ collides inelastically with a stationary $$3\ \mathrm{kg}$$ object. What is their final velocity after the collision?

Accepted Answer

$$v_f = \dfrac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \dfrac{5 	imes 4 + 3 	imes 0}{5 + 3} = \dfrac{20}{8} = 2.5\ \mathrm{m/s}$$

Question 7

A $$0.2\ \mathrm{kg}$$ ball is swung in a horizontal circle of radius $$0.5\ \mathrm{m} at a $$speed of $$3\ \mathrm{m/s}. $$What is the centripetal force acting on the ball?

Accepted Answer

$$F_c = \dfrac{mv^2$}{r} = \dfrac{0.2 	imes 9}{0.5} = 3.6\ \mathrm{N}$$

Question 8

A $$10\ \mathrm{kg}$$ box is pulled across a horizontal surface with a force of $$50\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. If the coefficient of kinetic friction is $$\mu_k = 0.2$$, what is the acceleration of the box?

Accepted Answer

$$a = \dfrac{F \cos 	heta - \mu_k mg}{m} = \dfrac{50 	imes 0.866 - 0.2 	imes 10 	imes 9.8}{10} \approx 0.13\ \mathrm{m/s^2$}$$

Question 9

A $$0.5\ \mathrm{kg}$$ mass attached to a string is whirled in a vertical circle of radius $$1\ \mathrm{m}. $$What is the minimum speed at the top of the circle to keep the string taut?

Accepted Answer

$$v_{min} = \sqrt{g r} = \sqrt{9.8 	imes 1} \approx 3.13\ \mathrm{m/s}$$

Question 10

A $$0.1\ \mathrm{kg}$$ ball is dropped from a height of $$2\ \mathrm{m}. $$What is its velocity just before hitting the ground?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 2} \approx 6.26\ \mathrm{m/s}$$

Question 11

A $$3\ \mathrm{kg}$$ object moves in a circle of radius $$2\ \mathrm{m} at a $$constant speed of $$5\ \mathrm{m/s}. $$What is the object's angular velocity?

Accepted Answer

$$\omega = \dfrac{v}{r} = \dfrac{5}{2} = 2.5\ \mathrm{rad/s}$$

Question 12

A $$0.5\ \mathrm{kg}$$ block is attached to a spring and oscillates with amplitude $$A = 0.2\ \mathrm{m}$$ and period $$T = 1\ \mathrm{s}. $$What is the maximum speed of the block?

Accepted Answer

$$v_{max} = \omega A = \dfrac{2\pi}{T} 	imes A = 2\pi 	imes 0.2 = 1.26\ \mathrm{m/s}$$

Question 13

A $$1\ \mathrm{kg}$$ object is dropped from rest and falls for $$3\ \mathrm{s}. $$What is its displacement?

Accepted Answer

$$y = \dfrac{1}{2} g t^2$ = \dfrac{1}{2} 	imes 9.8 	imes 9 = 44.1\ \mathrm{m}$$

Question 14

A $$2\ \mathrm{kg}$$ block slides $$5\ \mathrm{m}$$ across a horizontal surface with friction coefficient $$\mu_k = 0.3. $$How much work is done by friction?

Accepted Answer

$$W = -\mu_k m g d = -0.3 	imes 2 	imes 9.8 	imes 5 = -29.4\ \mathrm{J}$$

Question 15

A $$0.5\ \mathrm{kg}$$ mass is attached to a string and rotates in a horizontal circle of radius $$0.4\ \mathrm{m} at$$ $$6\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$T = \dfrac{mv^2$}{r} = \dfrac{0.5 	imes 36}{0.4} = 45\ \mathrm{N}$$

Question 16

A $$4\ \mathrm{kg}$$ object moving at $$3\ \mathrm{m/s}$$ collides elastically with a $$2\ \mathrm{kg}$$ object at rest. What is the velocity of the $$4\ \mathrm{kg}$$ object after the collision?

Accepted Answer

$$v_1$$' = \dfrac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \dfrac{4 - 2}{6} 	imes 3 = 1\ \mathrm{m/s}$$

Question 17

A $$0.3\ \mathrm{kg}$$ mass attached to a spring oscillates with frequency $$f = 2\ \mathrm{Hz}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = (2\pi f)^2$ m = (4\pi^2$) 	imes 0.3 \approx 11.84\ \mathrm{N/m}$$

Physics 2310 Syllabus and Course Structure: Classical Mechanics and Applications

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